Piece wise function help

f(x) =

x2 − 4

x − 2

if x < 2

ax2 − bx + 3

if 2 ≤ x < 3

4x − a + b

if x ≥ 3

OK guys so I'm having trouble with this, it includes a lot of algebra steps but I'll put some of them to show that I DID attempt it several times, not sure if I'm just tired or I messed up at some point....

Re: Piece wise function help

It should be clear that the function needs to approach 4 if you make x approach 2 from the left (why). For the function to be continuous at x = 2, it needs to approach the same value from the right. So that means .

For the function to be continuous at x = 3, we require the function to approach the same value from the left as from the right. So .

Simplify both of these equations and solve them simultaneously for a and b.